A decimal number can be converted into diffrent radices by continuos division and recording the remainders.
Part 1
To convert the decimal number 100 to radix 2, we have:
![\frac{100}{2} =50 \ remainder \ 0 \\ \\ \frac{50}{2} =25 \ remainder \ 0 \\ \\ \frac{25}{2} =12 \ remainder \ 1 \\ \\ \frac{12}{2} =6 \ remainder \ 0 \\ \\ \frac{6}{2} =3 \ remainder \ 0 \\ \\ \frac{3}{2} =1 \ remainder \ 1 \\ \\ \frac{1}{2} =0 \ remainder \ 1](https://tex.z-dn.net/?f=%20%5Cfrac%7B100%7D%7B2%7D%20%3D50%20%5C%20remainder%20%5C%200%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B50%7D%7B2%7D%20%3D25%20%5C%20remainder%20%5C%200%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B25%7D%7B2%7D%20%3D12%20%5C%20remainder%20%5C%201%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B12%7D%7B2%7D%20%3D6%20%5C%20remainder%20%5C%200%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B6%7D%7B2%7D%20%3D3%20%5C%20remainder%20%5C%200%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B3%7D%7B2%7D%20%3D1%20%5C%20remainder%20%5C%201%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B1%7D%7B2%7D%20%3D0%20%5C%20remainder%20%5C%201)
Starting from the bottom we collate the remainders.
Therefore, the value of decimal number 100 in radix 2 is
1100100
Part 2:
To convert the decimal number 100 to radix 3, we have:
![\frac{100}{3} =33 \ remainder \ 1 \\ \\ \frac{33}{3} =11 \ remainder \ 0 \\ \\ \frac{11}{3} =3 \ remainder \ 2 \\ \\ \frac{3}{3} =1 \ remainder \ 0 \\ \\ \frac{1}{3} =0 \ remainder \ 1](https://tex.z-dn.net/?f=%5Cfrac%7B100%7D%7B3%7D%20%3D33%20%5C%20remainder%20%5C%201%20%5C%5C%20%5C%5C%20%5Cfrac%7B33%7D%7B3%7D%20%3D11%20%5C%20remainder%20%5C%200%20%5C%5C%20%5C%5C%20%5Cfrac%7B11%7D%7B3%7D%20%3D3%20%5C%20remainder%20%5C%202%20%5C%5C%20%5C%5C%20%5Cfrac%7B3%7D%7B3%7D%20%3D1%20%5C%20remainder%20%5C%200%20%5C%5C%20%5C%5C%20%5Cfrac%7B1%7D%7B3%7D%20%3D0%20%5C%20remainder%20%5C%201)
Starting from the bottom we collate the remainders.
Therefore, the value of decimal number 100 in radix 3 is
10201
Part 3:
To convert the decimal number 100 to radix 4, we have:
![\frac{100}{4} =25 \ remainder \ 0 \\ \\ \frac{25}{4} =6 \ remainder \ 1 \\ \\ \frac{6}{4} =1 \ remainder \ 2 \\ \\ \frac{1}{4} =0 \ remainder \ 1](https://tex.z-dn.net/?f=%5Cfrac%7B100%7D%7B4%7D%20%3D25%20%5C%20remainder%20%5C%200%20%5C%5C%20%5C%5C%20%5Cfrac%7B25%7D%7B4%7D%20%3D6%20%5C%20remainder%20%5C%201%20%5C%5C%20%5C%5C%20%5Cfrac%7B6%7D%7B4%7D%20%3D1%20%5C%20remainder%20%5C%202%20%5C%5C%20%5C%5C%20%5Cfrac%7B1%7D%7B4%7D%20%3D0%20%5C%20remainder%20%5C%201)
Starting from the bottom we collate the remainders.
Therefore, the value of decimal number 100 in radix 4 is
1210
Part 4:
To convert the decimal number 100 to radix 5, we have:
![\frac{100}{5} =20 \ remainder \ 0 \\ \\ \frac{20}{5} =4 \ remainder \ 0 \\ \\ \frac{4}{5} =0 \ remainder \ 4](https://tex.z-dn.net/?f=%5Cfrac%7B100%7D%7B5%7D%20%3D20%20%5C%20remainder%20%5C%200%20%5C%5C%20%5C%5C%20%5Cfrac%7B20%7D%7B5%7D%20%3D4%20%5C%20remainder%20%5C%200%20%5C%5C%20%5C%5C%20%5Cfrac%7B4%7D%7B5%7D%20%3D0%20%5C%20remainder%20%5C%204)
Starting from the bottom we collate the remainders.
Therefore, the value of decimal number 100 in radix 5 is
400
Part 5:
To convert the decimal number 100 to radix 6, we have:
![\frac{100}{6} =16 \ remainder \ 4 \\ \\ \frac{16}{6} =2 \ remainder \ 4 \\ \\ \frac{2}{6} =0 \ remainder \ 2](https://tex.z-dn.net/?f=%5Cfrac%7B100%7D%7B6%7D%20%3D16%20%5C%20remainder%20%5C%204%20%5C%5C%20%5C%5C%20%5Cfrac%7B16%7D%7B6%7D%20%3D2%20%5C%20remainder%20%5C%204%20%5C%5C%20%5C%5C%20%5Cfrac%7B2%7D%7B6%7D%20%3D0%20%5C%20remainder%20%5C%202)
Starting from the bottom we collate the remainders.
Therefore, the value of decimal number 100 in radix 5 is
244
Part 6:
To convert the decimal number 100 to radix 7, we have:
![\frac{100}{7} =14 \ remainder \ 2 \\ \\ \frac{14}{7} =2 \ remainder \ 0 \\ \\ \frac{2}{7} =0 \ remainder \ 2](https://tex.z-dn.net/?f=%5Cfrac%7B100%7D%7B7%7D%20%3D14%20%5C%20remainder%20%5C%202%20%5C%5C%20%5C%5C%20%5Cfrac%7B14%7D%7B7%7D%20%3D2%20%5C%20remainder%20%5C%200%20%5C%5C%20%5C%5C%20%5Cfrac%7B2%7D%7B7%7D%20%3D0%20%5C%20remainder%20%5C%202)
Starting from the bottom we collate the remainders.
Therefore, the value of decimal number 100 in radix 5 is
202
Part 7:
To convert the decimal number 100 to radix 8, we have:
![\frac{100}{8} =12 \ remainder \ 4 \\ \\ \frac{12}{8} =1 \ remainder \ 4 \\ \\ \frac{1}{8} =0 \ remainder \ 1](https://tex.z-dn.net/?f=%5Cfrac%7B100%7D%7B8%7D%20%3D12%20%5C%20remainder%20%5C%204%20%5C%5C%20%5C%5C%20%5Cfrac%7B12%7D%7B8%7D%20%3D1%20%5C%20remainder%20%5C%204%20%5C%5C%20%5C%5C%20%5Cfrac%7B1%7D%7B8%7D%20%3D0%20%5C%20remainder%20%5C%201)
Starting from the bottom we collate the remainders.
Therefore, the value of decimal number 100 in radix 5 is
144
Part 8:
To convert the decimal number 100 to radix 9, we have:
![\frac{100}{9} =11 \ remainder \ 1 \\ \\ \frac{11}{9} =1 \ remainder \ 2 \\ \\ \frac{1}{9} =0 \ remainder \ 1](https://tex.z-dn.net/?f=%5Cfrac%7B100%7D%7B9%7D%20%3D11%20%5C%20remainder%20%5C%201%20%5C%5C%20%5C%5C%20%5Cfrac%7B11%7D%7B9%7D%20%3D1%20%5C%20remainder%20%5C%202%20%5C%5C%20%5C%5C%20%5Cfrac%7B1%7D%7B9%7D%20%3D0%20%5C%20remainder%20%5C%201)
Starting from the bottom we collate the remainders.
Therefore, the value of decimal number 100 in radix 5 is
121